Here, \(v_b\)  is the bubble wall velocity, the efficient factor \(\kappa \)  which characterizes the fraction of latent heat
deposited in a thin shell. We take \(\alpha \)  as a function of the phase strength parameter \(\alpha \)  [1]}:
\(\kappa \simeq \frac{0.715\alpha + \frac{4}{27} \sqrt{3\alpha /2}}{1+0.715\alpha } \;,\) 
